The present invention relates to a device in a meter for flow measurement, said meter comprising a casing which is made of a material having a known function of thermal expansion and through which a fluid passage extends, two transducers which are arranged acoustically opposite each other on a transducer mounting each and which are each adapted to repetitively transmit, essentially along a sound line and over a distance Lu between said transducers towards the opposite transducer, sound pulses in a fluid which in a direction flows through the fluid passage, and to receive sound pulses from the opposite transducer after passing through the fluid, and an electronic and calculation unit which is connected to said transducers for excitation and reading thereof and which is adapted to calculate, by means of the transit times of the sound pulses over the distance Lu between said transducers both concurrently with and countercurrently to the direction of flow of the fluid, a volume and/or mass flow and/or a velocity of flow of the fluid through the fluid passage.
Both the transit time and sing around technique are well-known techniques that are used, inter alia, in the measuring of flow rate and sonic velocity. FIG. 1 shows the principle of measuring by means of the sing around technique which differs from the transmit time technique mainly by its transmission of sound pulses which is repeated in a manner that will be described below. Through a fluid passage 2 arranged in a meter casing 1 flows a fluid at a velocity v which in the drawing is indicated by an arrow a which also indicates the main direction of flow from the left to the right. The passage 2 has two opposite branches both extending at an angle xcfx86 relative to the longitudinal axis of the passage and, thus, relative to the main direction of flow of the fluid. In each branch an ultrasonic transducer 5, 6 is mounted, which is inclined at an angle (90xc2x0xe2x88x92xcfx86) relative to the longitudinal axis of the passage 2. The transducers 5, 6 are interconnected by means of sing around electronics which is schematically shown in the form of a box 7.
With a view to measuring, for instance, the velocity v of the fluid in the passage 2, sing around loops are established both concurrently with and countercurrently to the direction of flow, which can take place simultaneously or preferably first in one direction, e.g. the upstream direction, by the sing around electronics 7 exciting the transducer 5 to transmit an ultrasonic pulse which is received by the transducer 6 after having passed through the fluid in the passage 2. When the sing around electronics 7 detects that the transducer 6 receives an ultrasonic pulse, it excites the transducer 5 to transmit a new ultrasonic pulse. The thus-established sing around loop is maintained for a predetermined number of turns N. Then the process is repeated in the downstream direction.
The sing around loop will oscillate with a certain period which is called the sing around period and which depends on the sonic velocity c in the fluid between the transducers, the distance Lu between the transducers and the flow velocity. The sing around period t1 in the downstream direction is given by:       t    1    =            L      u              c      +                        v          ·          cos                ⁢                  xe2x80x83                ⁢        φ            
and the sing around period t2 in the upstream direction is given by:       t    2    =            L      u              c      -                        v          ·          cos                ⁢                  xe2x80x83                ⁢        φ            
If the distance Lu between the transducers and the angle xcfx86 are known and the sing around periods t1 and t2 are measured, e.g. the flow velocity v can be determined according to the following formula:   v  =                    L        u                    2        ⁢                  xe2x80x83                ⁢        cos        ⁢                  xe2x80x83                ⁢        φ              ⁢          xe2x80x83        ⁢          (                        1                      t            1                          -                  1                      t            2                              )      
With the same information and with knowledge of the cross-sectional area and the form of the passage 2, also e.g. the volume flow rate in the passage 2 can be determined according to the following formula:   Vol  =            1      2        ⁢          xe2x80x83        ⁢                            AL          u                ⁢                  xe2x80x83                ⁢                  (                                    1                              t                1                                      -                          1                              t                2                                              )                            cos        ⁢                  xe2x80x83                ⁢        φ            
where Vol is the volume flow rate and A is the cross-sectional area of the fluid passage.
A drawback of the prior-art flow meters of the type in question is that both the distance Lu between the transducers and the cross-sectional area A of the fluid passage are temperature dependent. If thus the temperature of the fluid from an initial value T0 increases, for example, to a value T1, also the material of which the meter casing is made will be affected in course of time, which results in an increase of the distance Lu between the transducers and an increase of the cross-sectional area A. It will be appreciated that this fact must be taken into consideration especially when determining volume or mass flow rates since possible errors in such determination are potentiated.
In view of the above, the object of the present invention is to provide a device in a meter of the type mentioned by way of introduction, said device obviating the inaccuracies which temperature changes may cause in the meter.
According to the invention, this is achieved by a compensating means in the extension of the sound line being arranged between at least one of the transducer mountings and the associated transducer, said compensating means being made of a material having a known function of thermal expansion and having a length seen in the extension of the sound line so that a dimensional change, caused by a temperature change of the fluid, of the fluid passage along the distance between the transducer mountings, said dimensional change comprising a longitudinal change of the distance between the transducer mountings, is essentially compensated for by an opposite change, caused by the same temperature change, of the compensating means.
A person skilled in the art realises that such a compensating means is relatively easy to provide and dimension since the functions of thermal expansion of different materials are well documented and within reasonable temperature ranges have an essentially linear progress. It will also be appreciated that numeric calculation methods, such as finite element methods (FEM), can be used to calculate a suitable geometry of the compensating means for a given application. Moreover the person skilled in the art realises that by selecting materials having a greater function of thermal expansion for the compensating means, it is possible according to the invention to provide very compact but yet accurate meters, and that in spite of the choice of materials having a non-linear function of thermal expansion, such as plastics, it is according to the invention still possible to provide inexpensive meters with acceptable accuracy. Various embodiments of the invention, based on this knowledge, are defined in the dependent claims.
For an ultrasonic meter, which is of the diagonal type shown in FIG. 1 and has a fluid passage of circular cross-section, it is possible to express the distance Lu between said transducers as stated below, xcfx86 being the angle between the sound line l and the longitudinal axis of the fluid passage, Du being the transducer diameter, Dp being the diameter of the passage and xcex1p and xcex1t, respectively, being coefficients of thermal expansion of the passage and the compensating member, respectively, assuming a linear function of thermal expansion.       L    u    =                    Dp        ⁢                  (                      1            +                                          α                p                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              T                                )                            sin        ⁢                  xe2x80x83                ⁢        φ              +                  Du        ⁢                  (                      1            +                                          α                p                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              T                                )                            tan        ⁢                  xe2x80x83                ⁢        φ            
The cross-sectional area A can be expressed as:
A=xc2xcxcfx80Dp2(1+xcex1pxcex94T)2
This gives if eq=LuA:   eq  =            1      4        ⁢          xe2x80x83        ⁢          (                                    Dp            ⁢                          (                              1                +                                                      α                    p                                    ⁢                  Δ                  ⁢                                      xe2x80x83                                    ⁢                  T                                            )                                            sin            ⁢                          xe2x80x83                        ⁢            φ                          +                              Du            ⁢                          (                              1                +                                                      α                    p                                    ⁢                  Δ                  ⁢                                      xe2x80x83                                    ⁢                  T                                            )                                            tan            ⁢                          xe2x80x83                        ⁢            φ                              )        ⁢          xe2x80x83        ⁢    π    ⁢          xe2x80x83        ⁢                  "AutoLeftMatch"                              Dp            2                    ⁢                      (                          1              +                                                α                  p                                ⁢                Δ                ⁢                                  xe2x80x83                                ⁢                T                                      )                          "AutoRightMatch"            2      
The temperature dependence is illustrated by the derivative in respect of the temperature, eqd=diff (eq, xcex94T), i.e. a differentiation of eq in respect of xcex94T:   eqd  =                    1        4            ⁢              xe2x80x83            ⁢              (                                            Dp              ⁢                              xe2x80x83                            ⁢                              α                p                                                    sin              ⁢                              xe2x80x83                            ⁢              φ                                +                                    Du              ⁢                              xe2x80x83                            ⁢                              α                p                                                    tan              ⁢                              xe2x80x83                            ⁢              φ                                      )            ⁢              xe2x80x83            ⁢      π      ⁢              xe2x80x83            ⁢                        "AutoLeftMatch"                                    Dp              2                        ⁢                          (                              1                +                                                      α                    p                                    ⁢                  Δ                  ⁢                                      xe2x80x83                                    ⁢                  T                                            )                                "AutoRightMatch"                2              +                  1        2            ⁢              (                                            Dp              ⁢                              (                                  1                  +                                                            α                      p                                        ⁢                    Δ                    ⁢                                          xe2x80x83                                        ⁢                    T                                                  )                                                    sin              ⁢                              xe2x80x83                            ⁢              φ                                +                                    Du              ⁢                              (                                  1                  +                                                            α                      p                                        ⁢                    Δ                    ⁢                                          xe2x80x83                                        ⁢                    T                                                  )                                                    tan              ⁢                              xe2x80x83                            ⁢              φ                                      )            ⁢              xe2x80x83            ⁢      π      ⁢              xe2x80x83            ⁢              Dp        2            ⁢              (                  1          +                                    α              p                        ⁢            Δ            ⁢                          xe2x80x83                        ⁢            T                          )            ⁢              xe2x80x83            ⁢              α        p            
The cross-sectional area times the transducer distance, i.e. ALu, will obtain a temperature dependence owing to longitudinal expansion with the temperature. This will in turn cause an error in ultrasonic flow meters based on the transit time or sing around technique.
By introducing according to the invention a transducer with a compensating member which acts opposite to the temperature-dependent longitudinal changes of the fluid passage, this temperature dependence can be counteracted almost completely. Besides, if a material having a different coefficient of thermal expansion is used, the design of the transducer with the compensating member can be made very compact and simple. Introducing such a transducer with a compensating member having a length Lt in the expression for Lu gives the following expression for the transducer distance with a compensating member, Lku:       Lk    u    =                    Dp        ⁢                  (                      1            +                                          α                p                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              T                                )                            sin        ⁢                  xe2x80x83                ⁢        φ              +                  Du        ⁢                  (                      1            +                                          α                p                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              T                                )                            tan        ⁢                  xe2x80x83                ⁢        φ              +          2      ⁢                        L          t                ⁢                  (                      1            +                                          α                p                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              T                                )                      -          2      ⁢                        L          t                ⁢                  (                      1            +                                          α                t                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              T                                )                    
and if eqk=LkuA:   eqk  =            1      4        ⁢          xe2x80x83        ⁢          (                                    Dp            ⁡                          (                              1                +                                                      α                    p                                    ⁢                  Δ                  ⁢                                      xe2x80x83                                    ⁢                  T                                            )                                            sin            ⁢                          xe2x80x83                        ⁢            φ                          +                              Du            ⁡                          (                              1                +                                                      α                    p                                    ⁢                  Δ                  ⁢                                      xe2x80x83                                    ⁢                  T                                            )                                            tan            ⁢                          xe2x80x83                        ⁢            φ                          +                  2          ⁢                                    L              t                        ⁡                          (                              1                +                                                      α                    p                                    ⁢                  Δ                  ⁢                                      xe2x80x83                                    ⁢                  T                                            )                                      -                  2          ⁢                      L            t                    ⁢                      (                          1              +                                                α                  t                                ⁢                Δ                ⁢                                  xe2x80x83                                ⁢                T                                      )                              )        ⁢          xe2x80x83        ⁢                            Dp          2                ⁡                  (                      1            +                                          α                p                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              T                                )                    2      
By seeking the minima of the temperature dependence by differentiation of eqk in respect of xcex94T it is possible to determine how the components included are to be dimensioned to give a practically total independence of the temperature, thus eqd_k=diff(eqd, xcex94T):   eqd_k  =                    1        4            ⁢              xe2x80x83            ⁢              (                                            Dp              ⁢                              xe2x80x83                            ⁢                              α                p                                                    sin              ⁢                              xe2x80x83                            ⁢              φ                                +                                    Du              ⁢                              xe2x80x83                            ⁢                              α                p                                                    tan              ⁢                              xe2x80x83                            ⁢              φ                                +                      2            ⁢                          L              t                        ⁢                          α              p                                -                      2            ⁢                          L              t                        ⁢                          α              t                                      )            ⁢              xe2x80x83            ⁢      π      ⁢              xe2x80x83            ⁢                                    Dp            2                    ⁡                      (                          1              +                                                α                  p                                ⁢                Δ                ⁢                                  xe2x80x83                                ⁢                T                                      )                          2              +                  1        2            ⁢              xe2x80x83            ⁢              (                                            Dp              ⁡                              (                                  1                  +                                                            α                      p                                        ⁢                    Δ                    ⁢                                          xe2x80x83                                        ⁢                    T                                                  )                                                    sin              ⁢                              xe2x80x83                            ⁢              φ                                +                                    Du              ⁡                              (                                  1                  +                                                            α                      p                                        ⁢                    Δ                    ⁢                                          xe2x80x83                                        ⁢                    T                                                  )                                                    tan              ⁢                              xe2x80x83                            ⁢              φ                                +                      2            ⁢                                          L                t                            ⁡                              (                                  1                  +                                                            α                      p                                        ⁢                    Δ                    ⁢                                          xe2x80x83                                        ⁢                    T                                                  )                                              -                      2            ⁢                                          L                t                            ⁡                              (                                  1                  +                                                            α                      t                                        ⁢                    Δ                    ⁢                                          xe2x80x83                                        ⁢                    T                                                  )                                                    )            ⁢                        xe2x80x83                ⁢                  xe2x80x83                    ⁢      π      ⁢              xe2x80x83            ⁢                        Dp          2                ⁡                  (                      1            +                                          α                p                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              T                                )                    ⁢              xe2x80x83            ⁢              α        p            
If eqd_k is set at 0, and Lt is solved from this equation, the length (Lt)opt, which is suitable in this case, of the compensating member is obtained:             (              L        t            )        opt    =            3      2        ⁢          xe2x80x83        ⁢          α      p        ⁢                            Dp          ⁢                      xe2x80x83                    ⁢          tan          ⁢                      xe2x80x83                    ⁢          φ                +                  Dp          ⁢                      xe2x80x83                    ⁢                      α            p                    ⁢          Δ          ⁢                      xe2x80x83                    ⁢          T          ⁢                      xe2x80x83                    ⁢          tan          ⁢                      xe2x80x83                    ⁢          φ                +                  Du          ⁢                      xe2x80x83                    ⁢          sin          ⁢                      xe2x80x83                    ⁢          φ                +                  Du          ⁢                      xe2x80x83                    ⁢                      α            p                    ⁢          Δ          ⁢                      xe2x80x83                    ⁢          T          ⁢                      xe2x80x83                    ⁢          sin          ⁢                      xe2x80x83                    ⁢          φ                                      (                                    -                              α                p                                      -                          3              ⁢                              xe2x80x83                            ⁢                              α                p                2                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              T                        +                          α              t                        +                          3              ⁢                              xe2x80x83                            ⁢                              α                t                            ⁢                              α                p                            ⁢              Δ              ⁢                              xe2x80x83                            ⁢              T                                )                ⁢                  xe2x80x83                ⁢        tan        ⁢                  xe2x80x83                ⁢        φ        ⁢                  xe2x80x83                ⁢        sin        ⁢                  xe2x80x83                ⁢        φ            
It is thus obvious from that stated above that it is possible according to the invention to calculate, on the basis of known dimensional conditions of an otherwise arbitrary geometry at a reference temperature T0 and with knowledge of the functions of thermal expansion for the meter casing and the compensating means, a length Lt of the compensating means which is suitable in this case, and it will be appreciated that it is possible to optimise the design of the compensating means by taking into consideration, in the calculation, also the influence of temperature on the transducer diameter Du and the passage diameter Dp.
Moreover it will be appreciated that it is not necessary in all cases to use the compensating means to compensate for both cross-sectional and longitudinal changes. If, in view hereof, one wishes to compensate only for the temperature-dependent longitudinal changes of the fluid passage, it is possible to simplify the necessary calculations to a considerable extent. The conditions which have to prevail in that case can, based on the distance Lu between the above-mentioned transducers, be written as:
Lu=Lb(1+xcex1p(T0xe2x88x92T))xe2x88x922Lt(1+xcex1t(T0xe2x88x92T))
where Lb is the distance between the transducer mountings, Lt is the length of the compensating means, T0 is the current temperature, xcex1t is the function of thermal expansion of the compensating means and xcex1p is the function of thermal expansion of the casing. A differentiation of this equation in respect of temperature then gives:
xe2x80x83dLu=Lbxcex1bxe2x88x922Ltxcex1t
For dLu to be zero, the following must apply:
Lbxcex1b=2Ltxcex1t
thus:       L    t    =                    L        b            ⁢              α        b                    2      ⁢              xe2x80x83            ⁢              α        t            